Y AC ER M

NUMERACY
Y9
National Numeracy Tests
Procedural
sample
materials
Procedural sample materials: Guidance for teachers
The procedural tests will be first introduced in schools in 2013. Sample items have been
produced for each year group to illustrate different question types and formats for response.
The sample items are closely aligned to the numeracy framework and are representative of
the anticipated level of demand. However, they are not complete papers: the number of marks
within the tests next summer will range from about 28 for the lower year groups to about 36
for older learners. Each test will last 30 minutes.
How to use the sample items
The sample items can be printed and used for practice before the tests. Strengths and areas
for improvement can then be identified and used to provide additional classroom learning and
teaching activities, where appropriate.
●
The procedural sample items can also be used as a basis for classroom discussion, to illustrate
good test techniques. These include the importance of reading the question carefully, where
to write the answers, the relevance of showing working to gain partial credit, good time
management and the benefits of checking answers.
Teachers may wish to support learners by discussing different approaches towards 2 mark
items. For example, teachers could anonymise and photocopy a range of responses and ask
learners to work in small groups to rank from ‘best’ to ‘worst’, identifying what is good about
each and why.
Marking of the sample items
A markscheme is provided, which is typical of those to be used alongside the live tests.
It is designed to be quickly and fairly applied with clear guidance on when and how partial
credit should be applied. General marking guidance provides principles of marking to facilitate
consistency across schools.
●
2
1
37 + =1002
1m
– 25.6 = 53.9
1m
2
Write
80% as a decimal.
1m
Write
0.61 as a percentage.
%
1m
Write
23
4 as a mixed number.
1m
3
It takes David 1 hour and 30 minutes to drive 63 miles
from his home to Swansea.
What was his average speed?
miles per hour
2m
3
4
2 + 23=
1m
(12 – 9)2 + 8 ÷ 2 =
1m
5
Write
< , > or = in each box.
65%
0.66
1
4
0.4
2
40%
5
1
16
4%
2m
6
Work out the area of the circle.
10cm
Use π = 3.14
cm2
2m
4
7
Work out
13.8 × 0.2
2m
8
Dev and Anna each invested £500
After one year
Dev
Anna
£500
£500
decreased by
increased by
5%
15%
After one year, how much more does Anna have than Dev?
£
2m
5
9
33 – 32=
1m
10
What is the bearing of A from B?
N
130˚
A
N
°
1m
B
11
12
The reciprocal of 5 is
6
1m
104×105=
1m
6
13
£1.48 for
250 grams
How much for 2.75 kilograms?
£
2m
14
Work out 8667
÷ 27
2m
7
Procedural sample materials: Marking guidance
It is important that the tests are marked accurately. The questions and answers below help
to develop a common understanding of how to mark fairly and consistently.
Must learners use the answer boxes?
Provided there is no ambiguity, learners can respond anywhere on the page. If there is more
than one answer the one in the answer box must be marked, even if incorrect. However, if
the incorrect answer is clearly because of a transcription error (e.g. 65 has been copied as 56),
mark the answer shown in the working.
●
What if learners use a method that is not shown within the markscheme?
The markschemes show the most common methods, but alternative approaches may deserve
credit − use your best judgement. Any correct method, however idiosyncratic, is acceptable.
●
Does it matter if the learner writes the answer differently from that shown in the
markscheme?
Numerically equivalent answers (e.g. eight for 8, or two quarters or 0.5 for half) should be
marked as correct unless the markscheme states otherwise.
●
How should I mark answers involving money?
Money can be shown in pounds or pence, but a missing zero, e.g. £4.7, should be marked
as incorrect.
●
How should I mark answers involving time?
In the real world, specific times are shown in a multiplicity of ways so accept, for example,
02:30, 2.30, half past 2, etc. Do not accept 2.3 as this is ambiguous. The same principle should
be used for marking time intervals, e.g. for two and a half hours accept 2.5 but not 2.5pm.
●
What if the method is wrong but the answer is correct?
Unless the markscheme states otherwise, correct responses should be marked as correct even
if the working is incorrect as learners may have started again without showing their revised
approach).
●
What if the learner has shown understanding but has misread information in the question?
For a two (or more) mark item, if an incorrect answer arises from misreading information given
in the question and the question has not become easier as a result then deduct one mark only.
For example, if the 2 mark question is 86 × 67 and the learner records 96 × 67 then gives the
answer 6432, one mark only should be given. In a one mark question, no marks can be given.
●
What should I do about crossed out work?
Working which has been crossed out and not replaced can be marked if it is still legible.
●
What is the difference between a numerical error and a conceptual error?
A numerical error is one in which a slip is made, e.g. within 86 × 67 the learner works out
6 × 7 = 54 within an otherwise correct response. A conceptual error is a more serious
misunderstanding for which no method marks are available, for example if 86 × 60
is recorded as 516 rather than 5160
●
8
Year 9 Procedural sample materials: Markscheme
Q
Marks
1i
1m
965
1ii
1m
79.5
2i
1m
0.8
2ii
1m
61%
2iii
1m
5¾
3
2m
42 miles per hour
Or 1m
Answer
Comments
Do not accept equivalent
fractions
Do not accept equivalent
improper fractions
Correct method with only one numerical
error
4i
1m
10
4ii
1m
13
5
2m
<
Example for 1m:
63 ÷ 3 × 2 = 44 (error)
>
=
>
Or 1m
6
2m
Or 1m
7
2m
Or 1m
Any three answers correct
314cm2
π × 100 or 3.14 × 100 seen
2.76
Correct method with only one numerical
error
9
Example for 1m:
138 × 2 = 278 (error)
so answer 2.78
Q
Marks
8
2m
Or 1m
Answer
Comments
£100
20% of 500 seen
Or
25 or 475 seen
Or
75 or 575 seen
Or
Correct method with only one numerical
error
Example for 1m:
1% is 5 so 5% is 20 (error)
15% is 60 so she has 60 + 20 =
£80 more
9
1m
18
10
1m
310°
11
1m
65
Accept equivalent values, e.g.
1 15 or 1.2
12
1m
109
Accept 1000 000 000
13
2m
£16.28
Or 1m
1.48 × 11 seen
Or
Correct method with only one numerical
error
14
2m
Or 1m
Example for 1m:
1.48 × 10 = 14.80
14.80 + 1.48 = 15.28 (error)
321
Correct method with only one numerical
error
10
Example for 1m:
27 × 300 = 8100
27 × 20 = 540
27 × 1 = 27
8100 + 540 + 27 = 8667
so there are 311 (error)
© Crown copyright 2013